Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# If F ( X ) = 1 − 1 X , Then Write the Value of F ( F ( 1 X ) ) - Mathematics

If$f\left( x \right) = 1 - \frac{1}{x}$ , then write the value of $f\left( f\left( \frac{1}{x} \right) \right)$

#### Solution

Given:  $f\left( x \right) = 1 - \frac{1}{x}$
Now,  $f\left( \frac{1}{x} \right) = 1 - \frac{1}{\frac{1}{x}} = 1 - x$

$\Rightarrow f\left( f\left( \frac{1}{x} \right) \right) = f\left( 1 - x \right)$ Again,
If $f\left( x \right) = 1 - \frac{1}{x}$
Thus, $f\left( 1 - x \right) = 1 - \frac{1}{1 - x}$
$= \frac{1 - x - 1}{1 - x}$
$= \frac{- x}{1 - x}$
$= \frac{- x}{- \left( x - 1 \right)}$
$= \frac{x}{x - 1}$
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 3 Functions
Exercise 3.5 | Q 8 | Page 42